Systems known as “advanced” modulation systems such as the OFDM/OQAM, BFDM/OQAM, oversampled OFDM or else oversampled BFDM have numerous advantages over classic OFDM modulations.
First of all, these modulations have been designed to limit inter-symbol interference without the use of a guard interval in the time domain. These modulations therefore prevent any loss in spectral efficiency due to the introduction of a guard interval in OFDM.
Furthermore, these modulations allow introducing a waveform optimized with the appropriate criteria for a given transmission channel. In fact, the rectangular shaping of a signal done by classic OFDM modulation has the drawback of poor frequency localization.
Alternative solutions have therefore been proposed, leading to multiple-carrier modulation systems in which the signal is shaped by functions known as prototype functions that give better frequency localization.
Here below, a description is provided of the prior art pertaining to OFDM/OQAM (Offset Quadrature Amplitude Modulation) type modulations in which a QAM quadrature modulation implemented on each of the carriers is replaced by a modulation that offsets the real and imaginary parts of the complex symbols to be transmitted by a half symbol time for two successive carrier frequencies.
More specifically, FIG. 1 illustrates the main steps implemented for the OFDM/OQAM modulation according to the prior art.
As illustrated with reference to FIG. 1, the modulation scheme comprises data symbols at input representing a data signal to be transmitted. These data symbols denoted as am,n, carry a real value and are derived, at the symbol instant n and for the sub-carrier m, from usual preliminary operations not shown in FIG. 1.
These preliminary operations comprise the conversion of initial information data in binary form into data symbols. For example, in the case of a non-encoded system, a conversion known as a “binary to q-ary” conversion is performed. In the case of a 22K-state square constellation QAM (Quadrature Amplitude Modulation), where each state corresponds to a complex value, this conversion is a “binary to 2K-ary” type conversion. Then, as in the context of an OFDM/OQAM transmission, the real and imaginary parts are processed separately, and this amounts to having a one-dimensional K-state constellation where each possible state corresponds to a real value. In other words, the data symbols am,n are the result of a binary to K-ary PAM (Pulse Amplitude Modulation) type conversion.
These data symbols can correspond to payload data or to pilot data used for the channel estimation. When these pilots are inserted into the OFDM/OQAM signal in the form of an introduction, they are transmitted temporally before the payload data. For a channel that varies swiftly in time, these pilots are inserted permanently into the frame at temporal and frequency positions known to the sender and to the receiver.
In the case of OFDM/OQAM, the data symbols am,n undergo a pre-modulation 11. This pre-modulation step includes a complex multiplication operation on each subcarrier which makes it possible to take into account a phase term specific to the “QAM-2K to PAM-K” conversion as well as the length of the prototype filter.
The data symbols output from the pre-modulation block 11 are then converted from the frequency domain into the time domain by means of an inverse Fourier transform, also called IFFT 12.
The polyphase filtering operation 13 which follows the IFFT operation 12 corresponds to the application of the prototype filter in its form known as the polyphase form.
After a parallel/series conversion 14, at output of the modulator, the OFDM/OQAM signal denoted as s[k] is obtained in a discrete form, or s(t) in a continuous form after passing through a digital/analog converter 15.
More specifically, the OFDM/OQAM signal can be represented, in baseband, in the following form:
            s      ⁡              (        t        )              =                  ∑        n            ⁢                          ⁢                        ∑                      m            =            0                                M            -            1                          ⁢                                  ⁢                              a                          m              ,              n                                ⁢                                    g              ⁢                              (                                  t                  -                                      n                    ⁢                                                                                  ⁢                                          τ                      0                                                                      )                            ⁢                              ⅇ                                  j                  ⁢                                                                          ⁢                  2                  ⁢                                                                          ⁢                  π                  ⁢                                                                          ⁢                  m                  ⁢                                                                          ⁢                                      v                    0                                    ⁢                  t                                            ⁢                              ⅇ                                  jϕ                                      m                    ,                    n                                                                                      ︸                                                g                                      m                    ,                    n                                                  ⁡                                  (                  t                  )                                                                          ,
with:                am,n being the real-value data symbols to be transmitted on a sub-carrier m at the instant n;        M the number of carrier frequencies;        g the prototype function utilized by the modulator;        
            τ      0        =                  1        2            ⁢              T        0              ,                 with T0 the duration of a multicarrier signal at output of the modulator;        v0 the spacing between two adjacent subcarriers of the multiplex;        φm,n a phase term chosen so as to achieve a real part/imaginary part alternation enabling orthogonality or more generally bi-orthogonality.        
It can be noted that the steps implemented by the oversampled OFDM modulation are similar: pre-modulation 11, inverse Fourier transform 12, polyphase filtering 13, parallel/series conversion 14, and digital/analog conversion 15. However, the oversampled OFDM modulation scheme comprises data symbols at input denoted as cm,n, having a complex value. For example, these data symbols result directly from a “binary to 2K-ary” conversion.
Thus, the advanced modulations are used to achieve the desired conditions of orthogonality with prototype filters that are not necessarily rectangular, for example the IOTA (Isotropic Orthogonal Transform Algorithm) function. These modulation families thus offer a choice of prototype functions g wider than the simple rectangular prototype function of an OFDM modulation.
Thus, if the waveform g is chosen so as to meet the conditions of orthogonality known as real conditions, the real data symbols am,n transmitted by the OFDM/OQAM on a perfect channel are perfectly retrieved after demodulation, i.e. âm,n=am,n.
In the case of a transmission on a frequency-selective and time-selective channel, and for an appropriate size of the OFDM/OQAM system, if the function g is properly localized in time and frequency, one obtains âm,n≈am,n, assuming the application of a channel estimation technique that takes into account the specific nature of the orthogonality known as real orthogonality.
One drawback of these OFDM/OQAM type modulations is that the condition of orthogonality (or biorthogonality) is achieved only for real values of data symbols to be transmitted, creating a problem of estimation at reception and especially estimation of the transmission channel inasmuch as the received symbols are complex symbols.
More specifically, at reception, the OFDM/OQAM signal demodulated as (m0,n0) is obtained by ym0,n0(c)=y|gm0,n0, such that:
      y                  m        0            ,              n        0                    (      c      )        =                    H                              m            0                    ,                      n            0                                    (          c          )                    ⁢              a                              m            0                    ,                      n            0                                +                            ∑                                    (                              p                ,                q                            )                        ≠                          (                              0                ,                0                            )                                      ⁢                                  ⁢                              a                                                            m                  0                                +                p                            ,                                                n                  0                                +                q                                              ⁢                      H                                          m                0                            ,                              n                0                                                    (              c              )                                ⁢                                    〈              g              〉                                                                        m                  0                                +                p                            ,                                                n                  0                                +                q                                                                    m                0                            ,                              n                0                                                                ︸                  C                                    m              0                        ,                          n              0                                            +          D                        m          0                ,                  n          0                      +          b                        m          0                ,                  n          0                    where: gm0+p,n0+qm0n0 corresponds to a coefficient directly related to the ambiguity function of g,                Cm0,n0 is the interference term corresponding to the domain in which the channel is supposed to be constant;        Dm0,n0 is the interference term corresponding to the domain in which the channel is different;        bm0,n0 is the additive noise.        
For a low signal-to-noise ratio (SNR<30 dB), the interference term Dm0,n0 can be overlooked inasmuch as the noise is predominant. However, for a high SNR, the interference term Dm0,n0 becomes predominant, giving rise to the presence of a very high SNR error level.
Furthermore, the presence of an imaginary interference term at reception prevents the use of classic space/time encoding schemes increasing robustness in transmission.